The author develops a theory of Nöbeling manifolds similar to the theory of Hilbert space manifolds. He shows that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular the author proves the Nöbeling manifold characterization conjecture.

Table of Contents

Introduction and preliminaries

Introduction

Preliminaries

Reducing the proof of the main results to the construction of \(n\)-regular and \(n\)-semiregular \(\mathcal{N}_n\)-covers

Approximation within an \(\mathcal{N}_n\)-cover

Constructing closed \(\mathcal{N}_{n}\)-covers

Carrier and nerve theorems

Anticanonical maps and semiregularity

Extending homeomorphisms by the use of a "brick partitionings" technique